Question: The value of $\log_{10}{17}$ is between the consecutive integers $a$ and $b$.  Find $a+b$.
Explanation: We can have $\log_{10}10=1$ and $\log_{10}100=2$.  Since $\log_{10}x$ increases as $x$ increases, we know that $\log_{10}10<\log_{10}17<\log_{10}100$, meaning $1<\log_{10}17<2$.  Thus, the desired sum is $1+2=\boxed{3}$.